Parametric model reduction via interpolating orthonormal bases

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Abstract

In projection-based model reduction (MOR), orthogonal coordinate systems of comparably low dimension are used to produce ansatz subspaces for the efficient emulation of large-scale numerical simulation models. Constructing such coordinate systems is costly as it requires sample solutions at specific operating conditions of the full system that is to be emulated. Moreover, when the operating conditions change, the subspace construction has to be redone from scratch. Parametric model reduction (pMOR) is concerned with developing methods that allow for parametric adaptations without additional full system evaluations. In this work, we approach the pMOR problem via the quasi-linear interpolation of orthogonal coordinate systems. This corresponds to the geodesic interpolation of data on the Stiefel manifold. As an extension, it enables to interpolate the matrix factors of the (possibly truncated) singular value decomposition. Sample applications to a problem in mathematical finance are presented.

Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications : ENUMATH 2017
EditorsFlorin Adrian Radu, Kundan Kumar, Inga Berre, Jan Martin Nordbotten, Iuliu Sorin Pop
PublisherSpringer
Publication date5. Jan 2019
Pages683-691
ISBN (Print)978-3-319-96414-0
ISBN (Electronic)978-3-319-96415-7
DOIs
Publication statusPublished - 5. Jan 2019
EventEuropean Conference on Numerical Mathematics and Advanced Applications - University of Bergen, Voss, Norway
Duration: 25. Sep 201729. Sep 2017
http://www.uib.no/en/enumath2017

Conference

ConferenceEuropean Conference on Numerical Mathematics and Advanced Applications
LocationUniversity of Bergen
CountryNorway
CityVoss
Period25/09/201729/09/2017
Internet address
SeriesLecture Notes in Computational Science and Engineering
Volume126
ISSN1439-7358

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Zimmermann, R., & Debrabant, K. (2019). Parametric model reduction via interpolating orthonormal bases. In F. A. Radu, K. Kumar, I. Berre, J. M. Nordbotten, & I. S. Pop (Eds.), Numerical Mathematics and Advanced Applications: ENUMATH 2017 (pp. 683-691). Springer. Lecture Notes in Computational Science and Engineering, Vol.. 126 https://doi.org/10.1007/978-3-319-96415-7_63